=2. A scientist develops the logistic population model P' 0.2P(1) to describe her research data.This model has an equilibrium value of P = 8. In this model, from the initial condition Po = 4, thepopulation will never reach the equilibrium value because:(a) the population will grow toward infinity(b) the population is asymptotically approaching a value of 8.(c) the population will drop to 0Briefly describe how you determined your answer.

Let y′=f(y) be an autonomous differential equation, then the equilibrium values occur at f(y)=0.

Answered: = 2. A scientist develops the logistic…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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For a Pacific halibut population, the value of r is 0.71 per year, and the environmental carrying capacity is 89 thousand tons of fish.† (a) Find the time it takes the population to grow from the optimum yield level to 87% of carrying capacity if the number b in the logistic growth equation is 1.5. (Round your answer to three decimal places.) yr(b) Find the time it takes the population to grow from the optimum yield level to 87% of carrying capacity if the number b in the logistic growth equation is 4.8. (Round your answer to three decimal places.) yr
The demand for the Cyberpunk II arcade video game is modeled by the logistic curve 13,000 q(t) =- 1+0.6e-0,5: where g(?) is the total mumber of units sold t months after the game's introduction. Use technology to estimate q'(9). dR Assume that the manufacturers of Cyberpunk II sell each unit for $900. What is the company's marginal revenue, d Use the chain rule to estimate the rate at which revenue is growing 9 months after the introduction of the video game. Please round each answer to the nearest whole number. dą = 43, di dR = 900, dą dR = 38,478 a. dt dg Ob. = 143, di dR 900, dq dR = 128,260 di %3D dq dR dR C. di = 43, dq 900, = 38,734 dt dq = 86, dt dR = 800, dg dR d. = 76,956 dt dR O e. = 71, dr = 700, dą dR = 64,130 dt
Assume that the population of a town can be modeled by the logistic equation dP/dt = kP(1000 - P). If this town's population was 800 five years ago and is 850 this year, what is its population expected to be five years from now? Round your answer to the nearest integer.
Suppose the population of a species of animals on an island is governed by the logistic model with relative rate of growth k = 0.05 and carrying capacity M= 15000. I.e., the population function P(t) satisfies the equation P' = bP(15000 - P), where b = k/M. If the current population is P(0) = 20000, which one of the following is closest to P(1)? O a) 19700 O b) 19890 Oc) 19680 Od) 19690 Oe) 19805 Of) 19742 Motion
At time t = 0, a bacterial culture weighs 2 grams. Three hours later, the culture weighs 5 grams. The maximum weight of the culture is 20 grams. (a) Write a logistic equation that models the weight of the bacterial culture. (Round your coefficients to four decimal places.) 20 y = dy dt = 1 +9e 8 g (c) When will the culture's weight reach 16 grams? (Round your answer to two decimal places.) 9.79 hr (d) Write a logistic differential equation that models the growth rate of the culture's weight. Then repeat part (b) using Euler's Method with a step size of h = 1. (Round your answer to the nearest whole number.) y(5) = 6 -0.3662t = 1.37 0.366y| 1 (1-20) (b) Find the culture's weight after 5 hours. (Round your answer to the nearest whole number.) X g (e) At what time is the culture's weight increasing most rapidly? (Round your answer to two decimal places.) hr
Some of the highest tides in the world occur in the Bay of Fundy on the Atlantic Coast of Canada. At Hopewell Cape the water depth at low tide is about 2.0 m and at high tide it is about 12.0 m. The natural period of oscillation is a little more than 12 hours and on June 30, 2009, high tide occurred at 6:45 a.m. This helps explain the following model for the water depth D (in meters) as a function of time t (in hours after midnight) on that day: D(t) = 6 + 7 cos(0.503(t - 6.75)). How fast was the tide rising (or falling) at the following times? a. 6:00 a.m. b. 2:00 p.m.
I have tried 8 percent, 0.080, 0.079, and many others however I am still stuck on this problem. I even tried a different method that gave me 11.82 still wrong.
A study of Maryland's portion of Chesapeake Bay found the following information about stocks of market-sized oysters.† In 1994, the stocks were 218 million. (This is the number you will use for the initial population N(0).) The carrying capacity is 5089 million oysters. The intrinsic exponential growth rate is 0.274 per year. (a) Find a logistic model N(t) for the number, in millions, of market-sized oysters. Take t to be the time in years since 1994. (Rround all regression parameters to three decimal places.) N(t) = (b) Plot the graph of the model you found in part (a) over the first 20 years. (c) How many market-sized oysters does your model predict for 2007? Round your answer, in millions, to the nearest whole number. million oysters (d) The actual number of market-sized oysters was found to be 82 million. Use the Internet to find possible explanations for the reduced levels of oysters in Chesapeake Bay.
Assuming a carrying capacity for world population K = 15 billion, and a population of 7.75 billion as of 2020, estimate the year when population will reach 12 billion, assuming a logistic growth curve applies and with a current growth rate ro = 1.1% per year. What will the updated growth rate rf be in that future year when population reaches 12 billion?
The population, P, of kangaroos in a reservation is modelled by the logistic dP equation = dt 2P (5- reservation. - P 10 000 ) where t is measured in days. It is estimated that initially the population of the kangaroos is 15% of the carrying capacity of the (i) What is the initial population of the kangaroos? (ii) What is the population of the kangaroos when the rate of increase is a maximum?
During the period from 1790 to 1920, a country's population P(t) (t in years) grew from 3.6 million to 101.6 million. Throughout this period, P(t) remained close to the solution of the initial value problem -0.0001494P² P(0) = 3.6. dP dt = 0.03136P-( (a) What 1920 population does this logistic equation predict? (b) What limiting population does it predict? (c) The country's population in 2000 was 259 million. Has this logistic equation continued since 1920 to accurately model the country's population? (a) The logistic equation predicts the population in 1920 to be million. (Do not round until the final answer. Then round to the nearest thousandth as needed.) K AI C H TU U →> C ¢ ➡ H i O + 2.4 e В → نه Y + - 8 .... : *** 5 Ø Co Less . N 0 .. H A E X U i 9 A C ש Σ VI 8 FR > in X

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